We cannot (ultimately) explain everything

Amongst the many things science is useful for, explanation stands within the top. We use scientific knowledge to describe the world, to map it, to predict it, and to guide our actions thanks to the predictions about the consequences of our actions, but we also want science to provide us explanations, to help us understand why things are the way they are. Obviously, it is not only science what we use with that goal in mind: many people understand lots of things but don’t resort to anything we might call ‘science’ in the most specific sense of that word. I’m not just referring to religion believes, that obviously attempt to satisfy a big chunk of some people’s desire for understanding, but just to more mundane believes about ordinary things or actions: a mother understands what her daughter does, an entrepreneur understands why she has to invest in certain assets, a politician understands why it’s better to vote against some law, etc., etc., and all these cases of ‘understanding’ don’t need to be something like ‘applied scientific knowledge’, but often are even deteriorated when someone tries to replace them by something ‘more scientific’. But for questions that are distant from everyday interactions and common sense, science is of course the main, or even the only, provider of reasonable explanations.

The astonishing success of science in making us understand many difficult things has often led to the idea that we might (‘ideally’, at least) obtain a scientific explanation of everything. I will offer in this brief article a trivial proof of the impossibility of this goal: science cannot explain everything, nor even in ‘ideal’ circumstances. Obviously, this claim is not equivalent to saying that, if science cannot explain everything, then something else has to provide (and can provide) those explanations that are out of the reach of scientific thinking and scientific research. Quite the opposite, I will try to show that only scientific explanations can really count as true explanations, and hence, in those cases (outside the everyday, common sense ones of the type I mentioned above) where no scientific explanation can be provided, the truth is that no true explanation can be given.

1. What is to explain?

There is considerable debate within philosophy of science about what explanation really consists in. The most famous accounts are the ‘nomological’, the ‘causal’, and the ‘unificationist’, some of whose main defenders have been, respectively, the philosophers Carl Hempel, Wesley Salmon, and Philip Kitcher. According to the nomological (or ‘nomologico-deductive’) account of explanation, to explain a fact (or a regularity) is to deduce it from some more general laws, plus usually a set of ‘initial conditions’. The other two accounts were later developed in order to solve some cases in which we have deduction-from-laws but we think that there is no explanation (e.g., deducing the height of a tower from the length of its shadow, the angle of sun light, plus some optical laws). The causal approach adds the condition that the explanans must contain the true causes of the explanandum (and so, the effects can not ‘explain’ their causes), whereas the unificationist approach adds that one law only explains a phenomenon if it has ‘explanatory excess’, i.e, if it also explains other phenomena (or, stated differently, if it is not an ad hoc explanation): the more we can infer from one law or a system of laws, the more explanatory they are. Modern science, or so most contemporary philosophers assert, does not include other types of explanation typical of past worldviews or of common sense, like teleological or intentional explanations, which, if they are true explanations, must be reducible to general causal laws.

But, relevant as all these details are, the fact is that there is an element in the nomological account of explanation that all the other versions maintain: the necessary presence of laws or general regularities from which the explananda (the facts to be explained) are derived. Even in the causal account, which does not mention laws in some of its typical expositions, needs to resort to them in order to explicate what ‘causes’ consist in, for there is nothing like an individual event causing another individual event if we assume that there is not any kind of (deterministic or statistical) regularity connecting both types of events. Hence, there can be a set of conditions which makes of something an example of an explanation, but one of these conditions will be always within the explanans we have some law, regularity, principle, theory, etc., i.e., a statement having the logical form of a universal proposition (‘every time something like X happens, something like Y happens’… though Y may be the expression of some statistical distribution).

2. The impossibility of ultimate explanations.

Taking into account the nature of explanation and the unavoidability of laws in it, a trivial corollary is that there is something that cannot just be explained, viz., why the laws the universe obeys are the ones they are. For imagine that we have been able of discovering all the regularities that are true in the universe (this is impossible in practice, but suppose it is the case), and let S be the proposition asserting that all those regularities are true. The fact is that there is no possible explanation of why S is true. This is easy to show by a reductio ad absurdum argument: suppose there is a universal proposition T that can explain S. Since no proposition can explain itself (“because Newton gravitation law is true” is no acceptable answer to the question “why does matter obeys Newton gravitation law?”), T cannot be contained in S if T is to be explanatory of S. But, by hypothesis, S contained all the laws that are true in the universe, and hence, if S follows from T (what must be the case, for we have assumed that T explains S), T must be false, and cannot be the true explanation of why the universe is such that the regularities contained in S are true. In conclusion, the question ‘why the laws of the universe are the ones they are, instead of other possible laws’, is just a question that cannot be answered, at least with an answer which is true. Stated in other way: there is nothing like ‘the ultimate explanation of why the universe is the way it is’. The notion of ‘ultimate explanation’ is just a logical impossibility, taking into account what ‘explanation’ consists in.

A few clarifications are in order. The laws I have been referring to are always non-tautological statements, or contingent propositions, i.e., such that their negation involves no logical or mathematical contradiction. Of course, we can use logical or mathematical principles in our deductions of an explanandum from an explanans; but those principles do not contain the explanatory element of our explanations, they are only ways of showing that the (physical, empirical) laws included in our explanation have indeed (or have not) the consequences we want to derive from them. Logico-mathematical principles are true in all possible worlds, and what we want to explain is not why our world is a possible world (it is trivially one of them), but why it is the possible world it is, instead of a different possible world in which some propositions that are not logico-mathematical truths, but that are false in our universe, would be true. The dream of some scientists or philosophers, of explaining the world just out of mathematical principles, is just that, a dream; for the physical world could in principle have any possible mathematical structure (e.g., it could be isomorphic to system of positive real numbers, or to a mere couple of spheres orbiting each other; both cases are mathematically possible, i.e., they correspond to some mathematical structures, but these structures are not the structure of our physical world), whereas the aim of science is to show why the universe has the structure (or structures) it has, instead of other structures that, from the mathematical point of view, are just as consistent and possible as the actual structure of our universe.

Second, pseudo-explanations of the laws and existence of the universe, like the common ones amongst religious thinking (but not only there), either are not explanations at all (because they can not be used to logically infer what has to be explained, in the way Newtonian mechanics is able to infer Kepler’s laws about orbits or Galilei’s law of fall, which is the reason we say the former explains these) or use concepts (like ‘purpose’) that are manifestly incapable of providing the explanation we want to have (for ‘purpose’ has the meaning that there is a specific system that obeys some specific laws, and obeying these laws is what makes the system to behave in a way we can classify as ‘purposeful’; there is no difference between this concept and other like ‘digestion’ or ‘combustion’; why that system obeys the laws whose fulfilment is what makes of it a purposeful agent is something that, obviously, the purposes of the agent cannot explain). Something similar to this has recently been pointed out by Richard Dawkins: the information we want to explain must be contained in the theory with which we explain it, and hence, a theory that explains a lot of things must contain a lot of information, i.e., it must be in a deep sense a very detailed description of the working of the universe (or of that entity from which we attempt to explain the universe), though it can be ‘detailed’ in a very abstract sense.

Written by

Jesús Zamora holds PhDs in Philosophy (1993) and Economics (2001). Professor of Philosophy of Science and Director of the master's program on Science Communication and Journalism at UNED. Prolific author.